Elijah Lewis needs to determine how much to invest in a fund today that earns 6% interest in order to meet his daughter's college expenses for the next several years. To solve this problem, we will use the concept of the present value (PV) of a future amount, which discounts future cash flows to their present value using the formula:

$PV = \dfrac{FV}{(1 + r)^n}$

Where:

• $PV$ is the present value (the amount needed today).
• $FV$ is the future value (the payment required in the future).
• $r$ is the interest rate per period (6% or 0.06 in this case).
• $n$ is the number of periods (in years).

We'll calculate the present value of each future cash flow and sum them up to find the lump sum required today.

Step-by-step calculation:

1. Year 4: $24,000 $PV = \dfrac{24,000}{(1 + 0.06)^4} = \dfrac{24,000}{(1.06)^4}$

2. Year 5: $25,800 $PV = \dfrac{25,800}{(1 + 0.06)^5} = \dfrac{25,800}{(1.06)^5}$

3. Year 6: $27,300 $PV = \dfrac{27,300}{(1 + 0.06)^6} = \dfrac{27,300}{(1.06)^6}$

4. Year 7: $29,100 $PV = \dfrac{29,100}{(1 + 0.06)^7} = \dfrac{29,100}{(1.06)^7}$

Now, I'll calculate the individual present values and sum them to get the lump sum Elijah needs to invest today.Elijah Lewis needs to invest $76,888.09 today to meet his daughter's future college expenses.

Here are the present values of each future payment, rounded to the nearest cent:

1. Present value of $24,000 in 4 years: $19,010.25
2. Present value of $25,800 in 5 years: $19,279.26
3. Present value of $27,300 in 6 years: $19,245.42
4. Present value of $29,100 in 7 years: $19,353.16

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. How would the lump sum change if the interest rate was 5% instead of 6%?
2. What if the expenses were delayed by one year for each payment?
3. How much would Elijah need if his daughter requires an additional $10,000 in year 8?
4. What is the total amount paid in nominal terms without accounting for interest?
5. How would monthly contributions affect the total required?

Tip: Always account for the time value of money when planning for future payments!